Track1ConformalSchlaefliLocalExpansionEndpoint
plain-language theorem explainer
At lattice size N=5, the canonical conformal Schläfli along-line stationarity target follows from two concrete inputs: a global expansion/reindexing half and a local tetrahedral Schläfli identity at each parameter. Gravity Track 7 cites this as the localized Schläfli proof endpoint for Fork A handoff packaging. The declaration is a pure Prop abbreviation chaining those two antecedents to the full along-line target.
Claim. The localized conformal Schläfli endpoint at $N=5$ is the implication: if the canonical periodic conformal Schläfli along-line expansion/reindexing target holds at $N=5$, and the local tetrahedral conformal Schläfli along-line target holds at $N=5$, then the full canonical periodic conformal Schläfli along-line target holds at $N=5$.
background
Track 7 is the integration-lane receipt for parallel fork handoffs in the gravity master theorem. Fork A packages Track 1.B stationarity reduction at $N=5$; this endpoint is the localized Schläfli route inside that package. The module records what the new endpoints prove without upgrading the unconditional discovery claim, and keeps remaining Track 1 displacement-class leaves as open dependencies.
The three named targets are $N=5$ specializations of the six-tetrahedron cubic Dirichlet instance. The full along-line target asserts that the conformal Schläfli identity along the line closes the full stationarity target, bypassing per-displacement-class machinery. The expansion target is the global derivative/reindexing half of that route; the local target is the tetrahedral Schläfli identity at each parameter along the line. Both are non-flat concrete obligations feeding the same $N=5$ canonical periodic setting.
proof idea
No proof body: this is a definitional Prop, an implication arrow chain. It names the expansion target at $N=5$ and the local conformal Schläfli target at $N=5$ as antecedents, and the full along-line conformal Schläfli target at $N=5$ as consequent. Discharge is separate: the sibling theorem applies CanonicalPeriodicConformalSchlaefliAlongLineTargetAtN5_of_expansion_and_local to inhabit the Prop.
why it matters
This endpoint is the localized Schläfli proof interface consumed by Track 7. It feeds track1_conformal_schlaefli_local_expansion_endpoint_holds, the structure ForkHandoffIntegrationCert, and the one-statement integration theorem that packages Forks A–F for the master handoff. Downstream, Track 7 can consume Fork A's Schläfli-to-stationarity reduction package together with many-body, residual/Bianchi, Page-capacity, $w(z)$, and falsifier-sensitivity handoffs, while deliberately not asserting the fully unconditional discovery theorem.
In the Recognition gravity stack this is the clean reduction that lets conformal Schläfli along the line close stationarity at $N=5$ without walking every displacement class. Remaining open work sits on the Track 1 displacement-class leaves the module explicitly keeps as the next dependency.
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